Finite Group Databasebeta

← #35215686

Subgroups — #35215686

Order 20864.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19104726C211yesmaximal, characteristic
2C2×#19104660C211yesmaximal, characteristic
3C2×#19104658C211yesmaximal, characteristic
4#23781570C211yesmaximal, characteristic
5#23781427C211yesmaximal, characteristic
6#23781419C211yesmaximal, characteristic
7#340×C163C211yesmaximal, characteristic
8C22×Dic326C2211yescharacteristic
9C22×C163⋊C8C2211yescharacteristic
10#19104726—22no—
11#19104726—22no—
12C2×C4⋊Dic163—21no—
13C2×C4⋊Dic163C2211yescharacteristic
14C2×Dic163⋊C4—21no—
15C2×C4×Dic163C2211yescharacteristic
16#19104660—22no—
17#19104658—22no—
18C163⋊#95—21no—
19C163⋊#95—21no—
20C22×C8×C163C2211yescharacteristic
21C2×C4⋊C4×C163C2211yescharacteristic
22C2×C4⋊C4×C163C2211yescharacteristic
23C2×Dic326—21no—
24C2×Dic326—21no—
25C2×Dic326—21no—
26C2×Dic326—21no—
27C2×Dic326—21no—
28C2×Dic326Q812yes—
29C22×Dic163—21no—
30C22×Dic163—21no—
31C22×Dic163D411yescharacteristic
32C22×Dic163D411yescharacteristic
33C2×C163⋊C8—21no—
34C2×C163⋊C8—21no—
35C2×C163⋊C8—21no—
36C4⋊Dic163—24no—
37C4⋊Dic163—21no—
38C4⋊Dic163D412yes—
39Dic163⋊C4—24no—
40C4×Dic163—21no—
41C4×Dic163—21no—
42C22×C4×C163—21no—
43C22×C4×C163—21no—
44C22×C4×C163C2311yescharacteristic
45C2×C8×C163—21no—
46C2×C8×C163—21no—
47C2×C8×C163—21no—
48C4⋊C4×C163—21no—
49C4⋊C4×C163—21no—
50C4⋊C4×C163—21no—
51C4⋊C4×C163D412yes—
52Dic326—22no—
53Dic326—22no—
54Dic326—41no—
55Dic326—41no—
56C2×Dic163—21no—
57C2×Dic163—21no—
58C2×Dic163—22no—
59C2×Dic163—22no—
60C2×Dic163—21no—
61C2×Dic163—21no—
62C2×Dic163—21no—
63C2×Dic163—21no—
64C2×Dic163—41no—
65C2×Dic163—41no—
66C2×Dic163—41no—
67C2×Dic163—41no—
68C163⋊C8—41no—
69C23×C163C2×D411yescharacteristic
70C2×C4×C163—22no—
71C2×C4×C163—41no—
72C2×C4×C163—41no—
73C2×C4×C163—41no—
74C2×C4×C163—41no—
75C2×C4×C163—41no—
76C2×C4×C163C2×D411yescharacteristic
77C2×C4×C163C2×D411yescharacteristic
78C2×C4×C163C2×Q811yescharacteristic
79C2×C4×C163#4111yescharacteristic
80C2×C4×C163#4111yescharacteristic
81C2×C4×C163#4111yescharacteristic
82C8×C163—41no—
83C22×C163#12011yescharacteristic
84C22×C163C22⋊Q811yescharacteristic
85C22×C163#12411yescharacteristic
86C22×C163#13511yescharacteristic
87C22×C163#13511yescharacteristic
88C22×C163#13711yescharacteristic
89C22×C163#13711yescharacteristic
90C4×C163—42no—
91C4×C163—81no—
92C4×C163C22⋊Q811yescharacteristic
93C4×C163C22⋊Q811yescharacteristic
94C4×C163#12411yescharacteristic
95C4×C163#12411yescharacteristic
96Dic163—42no—
97Dic163—41no—
98Dic163—41no—
99Dic163—42no—
100C2×C163#39311yescharacteristic
101C2×C163#45211yescharacteristic
102C2×C163#45211yescharacteristic
103C2×C163#47911yescharacteristic
104C2×C163#47911yescharacteristic
105C2×C163#48811yescharacteristic
106C2×C163#49111yescharacteristic
107C163#202611yescharacteristic, complemented, Sylow
108#2026—1631nomaximal, Sylow
109C2×#125—1631no—
110C2×#103—1631no—
111C2×#103—1631no—
112#391—1631no—
113#340—1631no—
114#340D16311yescharacteristic
115#336—1631no—
116C22×Q8—1631no—
117C22×C8—1631no—
118C22×C8C2×D16311yescharacteristic
119#125—3262no—
120#125—3262no—
121C2×C4⋊C4—3261no—
122C2×C4⋊C4—3261no—
123C2×C4⋊C4—1631no—
124C2×C4⋊C4C2×D16311yescharacteristic
125C2×C4⋊C4C2×D16311yescharacteristic
126C2×C42—1631no—
127#103—3262no—
128#103—3262no—
129#95—3261no—
130#95—3261no—
131C2×Q8—3261no—
132C2×Q8—3261no—
133C2×Q8—3261no—
134C2×Q8—3261no—
135C2×Q8—3261no—
136C2×Q8—1632no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—3261no—
140C22×C4—3261no—
141C22×C4—1631no—
142C22×C4—1631no—
143C22×C4C22×D16311yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—3261no—
148C2×C8—3261no—
149C2×C8—3261no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—3264no—
154C4⋊C4—3264no—
155C4⋊C4—3261no—
156C4⋊C4—1632no—
157C4⋊C4D65212yes—
158C42—3261no—
159C42—3261no—
160C23D4×D16311yescharacteristic
161Q8—3262no—
162Q8—3262no—
163Q8—6521no—
164Q8—6521no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—3261no—
172C2×C4—3261no—
173C2×C4—3262no—
174C2×C4—3262no—
175C2×C4—3261no—
176C2×C4—3261no—
177C2×C4—3261no—
178C2×C4—3261no—
179C2×C4—6521no—
180C2×C4—6521no—
181C2×C4—6521no—
182C2×C4—6521no—
183C2×C4D4×D16311yescharacteristic
184C2×C4C2×D65211yescharacteristic
185C2×C4Q8×D16311yescharacteristic
186C2×C4#1457969811yescharacteristic
187C2×C4#1457969911yescharacteristic
188C2×C4#1457969911yescharacteristic
189C8—41no—
190C8—6521no—
191C22#1910470511yescharacteristic
192C22#1910471311yescharacteristic
193C22#1910472111yescharacteristic
194C22#1910475411yescharacteristic
195C22#1910475611yescharacteristic
196C22#1910476411yescharacteristic
197C22#1910476711yescharacteristic
198C4—42no—
199C4—81no—
200C4—6521no—
201C4—6521no—
202C4—6522no—
203C4—6522no—
204C4#1910471311yescharacteristic
205C4#1910471511yescharacteristic
206C4#1910472111yescharacteristic
207C4#1910472311yescharacteristic
208C2#2378157811yescharacteristic
209C2#2378182811yescharacteristic
210C2#2378183011yescharacteristic
211C2#2378197111yescharacteristic
212C2#2378197511yescharacteristic
213C2#2378201811yescharacteristic
214C2#2378203211yescharacteristic
subgroupG/H
centerC23D4×D163
commutator, cosocleC22×C4×C163C23
FrattiniC22×C4C22×D163
Fitting#340×C163C2
socle, prime radicalC23×C163C2×D4
hypercenter#340D163
hypocenterC163#2026
LCSG ▷ C22×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
107. C163#2026semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191047262
C2×#191046602
C2×#191046582
#237815702
#237814272
#237814192
#340×C1632
#2026163